Device and method for quantitatively characterizing flow conductivity under non-uniform sanding condition

Abstract

The invention discloses a device and method for quantitatively characterizing flow conductivity under a non-uniform sanding condition, and relates to the technical field of oil and gas exploitation, the device comprises a liquid supply mechanism, a bearing plate and a cover plate, a groove is formed in the bearing plate, and the cover plate is arranged at a groove opening of the groove in a sealing and covering mode; a groove is formed in one side wall of the bearing plate, a plurality of sand paving areas used for paving different amounts of quartz sand are arranged in the groove in a grid shape, a plurality of holes used for simulating wellbore perforation are formed in the side wall of the bearing plate, a liquid inlet hole is formed in the other side wall of the bearing plate and communicates with a liquid supply mechanism, and the liquid inlet hole and the holes communicate with the groove; according to the method, different quantities of quartz sand are paved in the sand paving area, a non-uniform sand paving working condition is formed, a non-uniform sand body structure formed by fluid shearing and pump starting and stopping impact in an actual reservoir stratum is truly simulated, and meanwhile, the simulation trueness is improved and the final characterization accuracy is improved in cooperation with a hole for simulating a perforation.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploitation, and particularly relates to a device and method for quantitatively characterizing the conductivity under non-uniform sand placement conditions. Background Art

[0002] In the fracturing operation of oil and gas fields, the evaluation of the conductivity of proppants is a key link in optimizing production capacity. For a long time, experimental studies have generally been based on idealized uniform sand placement models, using mechanical leveling or single-size sand bodies to simulate the distribution of proppants. Such simplified assumptions can lead to a deviation of 30%-50% between the conductivity data and the actual working conditions. Especially during the wellbore backflow process, when the proppants undergo secondary migration due to an asymmetric flow velocity field, the prediction error of traditional methods is more significant.

[0003] Currently, the commonly used experimental research devices include an experimental cavity filled with quartz sand as proppants. By introducing water into the experimental cavity for reflux simulation, the overall experimental device separates the proppant migration and conductivity into static, homogeneous, and single-scale research categories, with a low simulation authenticity, resulting in a reduction in the characterization accuracy.

[0004] Therefore, there is an urgent need for a device that can quantitatively characterize the conductivity under non-uniform sand placement conditions with high simulation authenticity and high characterization accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a device and method for quantitatively characterizing the conductivity under non-uniform sand placement conditions to solve the problems existing in the above-mentioned prior art. By laying unequal amounts of quartz sand in the sand placement area to form a non-uniform sand placement condition, simulating the real non-uniform sand body structure, and cooperating with the perforations simulating wellbore perforation, the simulation authenticity is improved, and the accuracy of the final characterization is enhanced.

[0006] To achieve the above purpose, the present invention provides the following solution: The present invention provides a device for quantitatively characterizing the conductivity under non-uniform sand placement conditions, including a liquid supply mechanism, a carrier plate, and a cover plate. The carrier plate is provided with a groove, the cover plate is hermetically covered at the notch of the groove, and a plurality of sand placement areas for laying unequal amounts of quartz sand are arranged in a grid pattern inside the groove. A plurality of holes for simulating wellbore perforation are provided on the side wall of the carrier plate, and a liquid inlet hole is provided on the other side wall of the carrier plate. The liquid inlet hole is communicated with the liquid supply mechanism, and both the liquid inlet hole and the holes are communicated with the groove.

[0007] Preferably, the amount of sand in the sand placement area near the holes is greater than that in the sand placement area far from the holes.

[0008] Preferably, the cover plate is a transparent cover plate.

[0009] Preferably, a camera is provided above the cover plate, and the camera is connected to the computer.

[0010] Preferably, a plurality of depressions are unevenly arranged at the bottom of the groove.

[0011] Preferably, a grid-shaped insertion plate is detachably arranged in the groove, and the grid area of the grid-shaped insertion plate matches the sand-laying area.

[0012] Preferably, an angle rotation mechanism is arranged at the bottom of the bearing plate. The angle rotation mechanism includes a support, a column, and a support plate. The support plate is rotatably arranged on the column, and a locking mechanism is arranged at the rotation position. The bearing plate is connected to the support plate.

[0013] Preferably, a plurality of liquid inlet holes are arranged on the bearing plate, and the plurality of liquid inlet holes are arranged in sequence from the near-well side to the far-well side. The liquid supply mechanism includes a pump body, a multi-way valve, and a plurality of branch pipelines respectively communicated with the liquid inlet holes. The plurality of branch pipelines are all communicated with the pump body through the multi-way valve. The pump body is communicated with a liquid tank, a main valve is arranged between the pump body and the multi-way valve, and a regulating valve, a flowmeter, and a pressure gauge are arranged on the branch pipeline.

[0014] Preferably, an intermediate container is arranged between the pump body and the multi-way valve. The inner cavity of the intermediate container is divided into a first cavity and a second cavity by a piston. The pump body and the multi-way valve are respectively communicated with the first cavity and the second cavity.

[0015] The present invention also provides a method for applying the device for quantitatively characterizing the diversion capacity under non-uniform sand-laying conditions as described above, including the following steps: S1: Lay unequal amounts of quartz sand in a plurality of sand-laying areas of the groove, and cover the cover plate; S2: Start the liquid supply mechanism to supply liquid into the groove, and the liquid flows through the sand-laying area and then flows out from the holes; S3: Obtain the sand bed permeability and the inlet and outlet pressure difference according to the change of the inlet and outlet liquid pressure of the groove, obtain the flow cross-sectional area and the sand bed length by using the size of the groove, and finally calculate the sand bed diversion capacity; S4: Close the liquid supply mechanism, open the cover plate, and obtain the proppant migration law according to the remaining amount of quartz sand in the sand-laying area.

[0016] The present invention mainly achieves the following technical effects compared with the prior art: By laying unequal amounts of quartz sand in the sand-laying area, a non-uniform sand-laying working condition is formed, which truly simulates the non-uniform sand body structure formed by fluid shear and pump start-stop impact in the actual reservoir. At the same time, in cooperation with the holes simulating perforation, the simulation authenticity is improved, and the accuracy of the final characterization is improved.

[0017] The following technical effects are achieved by other solutions of the present invention compared with the prior art: The design of the sand volume distribution on the near-well side and far-well side, the design of the depression, and the design of the angle rotation mechanism can further simulate the sand body structure in the actual reservoir and simulate different fracture angles, improving the simulation authenticity.

[0018] The design of the transparent cover plate makes the experimental process visual. With the setting of the camera, the redistribution trajectory of the proppant particles under the condition of proppant backflow and the microscopic behavior of embedding into the fracture wall can be effectively captured.

[0019] By controlling the multi-way valve and adjusting the valve, the liquid can be fed through different liquid inlet holes and the flow rate can be regulated, achieving local fine control and realizing the purpose of regulating the flow rate in different regions. The different flow rates in the near-well zone and far-well zone under real formation conditions can be simulated, improving the simulation authenticity. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a schematic structural diagram of the device for quantitatively characterizing the conductivity under non-uniform sand placement conditions in the embodiments of the present invention; Figure 2 It is a schematic structural diagram of the carrier plate and the cover plate in the embodiments of the present invention; Figure 3 It is a schematic structural diagram of the angle rotation mechanism in the embodiments of the present invention; Figure 4 It is a schematic structural diagram of the cover plate being sealed by the top bolts and the sealing strips in the embodiments of the present invention; Among them, 1. Carrier plate; 2. Cover plate; 3. Liquid inlet hole; 4. Hole; 5. Camera; 6. Computer; 7. Pump body; 8. Intermediate container; 9. Piston; 10. Main valve; 11. Multi-way valve; 12. Branch pipeline; 13. Pressure gauge; 14. Flowmeter; 15. Groove; 16. Depression; 17. Support plate; 18. Column; 19. Support; 20. Top bolt; 21. Horizontal strip hole; 22. Sealing strip. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0023] The purpose of the present invention is to provide a device and method for quantitatively characterizing the flow conductivity under non-uniform sand placement conditions, so as to solve the problems existing in the prior art. By laying unequal amounts of quartz sand in the sand placement area, a non-uniform sand placement working condition is formed to simulate the real non-uniform sand body structure. At the same time, in cooperation with the perforation holes for simulating perforation, the simulation authenticity is improved, and the accuracy of the final characterization is improved.

[0024] In order to make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Please refer to as Figures 1 to 4 shown, there is provided a device for quantitatively characterizing the flow conductivity under non-uniform sand placement conditions, including a liquid supply mechanism, a bearing plate 1 and a cover plate 2. The bearing plate 1 can be an iron bearing plate or a stainless steel bearing plate, etc. A groove 15 is formed on the bearing plate 1. The horizontal cross-section of the groove 15 is square or rectangular in shape, etc. The cover plate 2 is hermetically covered at the notch of the groove 15. A plurality of sand placement areas for laying unequal amounts of quartz sand are arranged in a grid pattern inside the groove 15. The thicknesses of the quartz sand in the finally formed plurality of sand placement areas are all different; a plurality of holes 4 for simulating wellbore perforation are formed on the side wall of the bearing plate 1. A liquid inlet hole 3 is formed on the other side wall of the bearing plate 1. The liquid inlet hole 3 is communicated with the liquid supply mechanism. Both the liquid inlet hole 3 and the holes 4 are communicated with the groove 15. By laying unequal amounts of quartz sand in the sand placement area, a non-uniform sand placement working condition is formed to truly simulate the non-uniform sand body structure formed in the actual reservoir due to fluid shear and pump start-stop impact. At the same time, in cooperation with the holes 4 for simulating perforation, the simulation authenticity is improved, and the accuracy of the final characterization is improved.

[0026] The specific structure of the cover plate 2 is as follows: The cover plate 2 includes a substrate and a protrusion. The protrusion is matched with the groove 15 and is embedded in the groove 15. The edge of the substrate covers the edge of the carrier plate 1, and a sealing gasket is provided between the two; or the cover plate 2 itself is matched with the groove 15, and a sealing ring is provided at the notch of the groove 15. After the cover plate 2 is embedded in the groove 15, the sealing ring is squeezed to achieve sealing; or the width of the cover plate 2 is designed to be matched with the groove 15, and the length is slightly shorter than the length of the groove 15. A tightening bolt 20 is threadedly connected to the side wall in the length direction of the carrier plate 1. The bolt extends into a horizontal strip-shaped hole 21 opened on the inner wall of the groove 15. A sealing strip 22 is provided in the horizontal strip-shaped hole 21. The sealing strip 22 has the same side length as the side of the cover plate 2 in contact with it. By screwing the tightening bolt 20, the sealing strip 22 can be squeezed to contact the cover plate 2 for sealing. Sealing strips can also be provided between the other three sides of the cover plate 2 except the side in contact with the sealing strip 22 and the inner wall surface of the groove 15; or other structures that can achieve the sealed connection between the cover plate 2 and the groove can be adopted.

[0027] A handle can be provided on the cover plate 2 to facilitate lifting the cover plate 2.

[0028] In this embodiment, the horizontal cross-section of the groove 15 is designed to be square, and the cavity of the groove 15 is divided into a grid-like space of 10x10. Each grid is a sand-laying area; in other embodiments, grooves 15 of other shapes can also be selected, and their cavities are divided into grid-like spaces of different specifications.

[0029] The amount of sand in the sand-laying area near the hole 4 is greater than that in the sand-laying area far from the hole 4. Taking the sand-laying areas distributed in a grid pattern as an example, there are multiple columns of sand-laying areas distributed upward along the hole 4. The amount of sand in multiple sand-laying areas in each column decreases in sequence along the direction away from the hole 4, so as to simulate the sand body structure in the actual reservoir and improve the simulation authenticity.

[0030] The cover plate 2 can be designed as a transparent cover plate 2, which is made of transparent materials such as glass and acrylic, and can make the experimental process visual.

[0031] A camera 5 is provided above the cover plate 2. The camera 5 is connected to a computer 6. During the experiment, the camera 5 can take pictures of the inside of the groove 15 every few seconds and transmit them to the computer 6, which can effectively capture the redistribution trajectory of the proppant particles under the condition of proppant backflow and the microscopic behavior of embedding the fracture wall surface.

[0032] A plurality of depressions 16 are unevenly arranged at the bottom of the groove 15 to further simulate the sand body structure in the actual reservoir and improve the simulation authenticity.

[0033] Since it is necessary to weigh the quartz sand in the sand-laying area before and after the experiment to determine the migration amount of the quartz sand, and then judge the stability of the sand body. In order to accurately measure the quartz sand in each sand-laying area, a grid-shaped insert plate is detachably arranged in the groove 15. The grid area of the grid-shaped insert plate matches the sand-laying area. The grid-shaped insert plate can divide the groove 15 into multiple sand-laying areas. Before sand-laying, it is used to lay sand in different areas in cooperation with the grid-shaped insert plate. After sand-laying is completed, the grid-shaped insert plate is taken out. After the experiment is completed, the grid-shaped insert plate is inserted again to take sand in different areas.

[0034] An angle rotation mechanism is arranged at the bottom of the bearing plate 1. The angle rotation mechanism includes a support 19, a column 18 and a support plate 17. The support plate 17 is rotatably arranged on the column 18, and a locking mechanism is arranged at the rotation position. The bearing plate 1 is connected to the support plate 17. By adjusting the angle of the bearing plate 1, different fracture angles can be simulated, improving the simulation authenticity. The locking mechanism is selected according to the rotational connection mode between the support plate 17 and the column 18. For example, the support plate 17 and the column 18 are connected by a ball joint. The ball joint includes a seat body with a spherical groove and a spherical ball rotating in the spherical groove. The seat body and the spherical ball are respectively connected to the support plate 17 and the column 18. A locking bolt is arranged on the seat body as the locking mechanism. The locking bolt is threadedly connected to the seat body and can extend into the spherical groove to abut against the spherical ball. Or a horizontal rotation hole is arranged on the column 18. A horizontal rotation shaft is connected to the bottom of the support plate 17 through a connecting rod. The rotation shaft rotates in the rotation hole, and the end far from the connecting rod extends out of the rotation hole. A thread is arranged on the extended part of the rotation shaft, and a locking nut is threadedly connected. By screwing the locking nut, the nut and the connecting rod respectively abut against both ends of the column 18 to achieve locking. The nut is the locking mechanism.

[0035] A plurality of liquid inlet holes 3 are arranged on the bearing plate 1. The plurality of liquid inlet holes 3 are arranged in sequence from the near-well side to the far-well side. The liquid supply mechanism includes a pump body 7, a multi-way valve 11 and a plurality of branch pipelines 12 respectively communicated with the liquid inlet holes 3. The plurality of branch pipelines 12 are all communicated with the pump body 7 through the multi-way valve 11. The pump body 7 is communicated with a liquid tank. A main valve 10 is arranged between the pump body 7 and the multi-way valve 11 to control the total liquid delivery. An adjusting valve, a flow meter 14 and a pressure gauge 13 are arranged on the branch pipeline 12. By controlling the multi-way valve 11, different liquid inlet holes 3 can be selected for liquid inlet. By controlling the adjusting valve, the flow rate can be regulated. The design of multiple branches achieves local fine control and realizes the purpose of regulating the flow rate in different areas. It can simulate the situation where the flow rates in the near-well area and the far-well area are different under real formation conditions, improving the simulation authenticity.

[0036] An intermediate container 8 is provided between the pump body 7 and the multi-way valve 11. The inner cavity of the intermediate container 8 is divided into a first cavity and a second cavity by a piston 9. The pump body 7 and the multi-way valve 11 are respectively communicated with the first cavity and the second cavity. The liquid pressurized by the pump body 7 enters the first cavity, and the pressure is applied to the piston 9 to push the piston 9 to move, so as to realize the input of the liquid in the second cavity into the subsequent multi-way valve 11 and the branch pipeline 12; the liquid selected in this embodiment is water.

[0037] The present invention also provides a method for applying the device for quantitatively characterizing the diversion capacity under non-uniform sand laying conditions, which is characterized by including the following steps: S1: Lay unequal amounts of 40 / 70-mesh quartz sand in multiple sand laying areas of the groove 15, cover the cover plate 2, and then adjust the angle of the bearing plate 1 by adjusting the angle between the support plate 17 and the column 18; turn on the camera 5 and the computer 6 to prepare for the experiment; S2: Select the branch pipeline 12 that needs to pass water, start the pump body 7 to supply liquid into the groove 15, and the liquid flows out from the hole 4 after flowing through the sand laying area. In this step, the water flow rate entering the groove 15 can be regulated by regulating the regulating valve on the branch pipeline 12; the camera continuously captures the image information during the experiment; S3: Obtain the sand bed permeability and the inlet and outlet pressure difference according to the change of the inlet and outlet liquid pressure of the groove 15, obtain the flow cross-sectional area (the horizontal cross-sectional area of the groove 15) and the sand bed length (the length of the groove 15 along the upward direction of the liquid inlet hole 3) by using the size of the groove 15, and finally calculate the sand bed diversion capacity; S4: Close the liquid supply mechanism, open the cover plate 2, calculate the mass transfer rate according to the remaining amount of quartz sand in the sand laying area, and obtain the proppant migration law.

[0038] In step S2, the uniformity of the sand laying during the experiment can be obtained according to the images obtained by the camera 5, and the specific principle is as follows: First, divide the obtained images into grids according to the distribution of the sand laying areas, and then calculate the average gray value in each grid. The calculation method is:

[0039] Then, establish a mathematical relationship between the gray value and the density according to the sand samples with known densities (calibration through experiments is required in advance).

[0040] The calibration method is: Prepare multiple sand samples with known densities (such as loose, medium, and dense), photograph and measure their average gray values, and fit the curve. For example, the calibration formula is:

[0041] Where a and b are coefficients fitted through calibration experiments (when the gray value is lower and the density is higher, a is negative).

[0042] According to the obtained density information, take the difference between the highest and lowest density areas and compare the overall average density. The calculation formula is:

[0043] Where DDI is the density difference index, ρ max is the highest value of density, ρ min is the minimum density, ρ 平均 is the average density.

[0044] Definition classification: If DDI is less than 20%, the computer 6 marks the sand body photo as green, which is defined as uniform sand spreading; 20% less than DDI less than 40%, the computer 6 marks the sand body photo as yellow, which is defined as moderately non-uniform sand spreading; DDI is greater than 40%, the computer 6 marks the sand body photo as red, which is defined as non-uniform sand spreading.

[0045] In step S3, the conductivity is characterized by the Darcy correction formula. This model can accurately quantify the dynamic relationship between sand bed stability and conductivity under non-uniform sand spreading conditions, providing a direct basis for optimizing fracturing operation parameters. The conductivity calculation formula is as follows:

[0046] Where Fc is the conductivity, k is the sand bed permeability, A is the flow cross-sectional area, P is the pressure difference between the liquid inlet hole 3 and the hole 4, L is the length of the sand bed, and μ is the fluid viscosity.

[0047] In step S4, the corresponding calculation formula is:

[0048] Where MR is the mass mobility, m 迁移 is the mass of quartz sand in the sand-paving area after the experiment, m 初始 It is the quality of quartz sand in the sand-paved area after the experiment. When MR>15%, it means that the sand body has been significantly reconstructed and this area needs to be analyzed in detail. When MR<5%, it means that the sand bed is stable.

[0049] Adaptive changes made according to actual needs are all within the protection scope of the present invention.

[0050] It should be noted that for those skilled in the art, it is obvious that the present invention is not limited to the details of the above-described exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims involved.

[0051] Specific examples are used in the present invention to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions, characterized in that: It includes a liquid supply mechanism, a bearing plate and a cover plate, the bearing plate is provided with a groove, the cover plate sealing cover is arranged at the notch of the groove, a plurality of sand-laying areas for laying unequal amounts of quartz sand are arranged in a grid shape inside the groove, a plurality of holes for simulating wellbore perforation are provided on the side wall of the bearing plate, a liquid inlet hole is provided on the other side wall of the bearing plate, the liquid inlet hole is connected with the liquid supply mechanism, and the liquid inlet hole and the holes are both connected with the groove.

2. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: The amount of sand in the sand-spreading area close to the hole is greater than the amount of sand in the sand-spreading area far from the hole.

3. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: The cover plate is a transparent cover plate.

4. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 3, characterized in that: A camera is arranged above the cover plate and is connected to a computer.

5. The device for quantitatively characterizing flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: The bottom of the groove is unevenly provided with a plurality of depressions.

6. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: A grid-shaped plug plate is detachably arranged in the groove, and a grid area of ​​the grid-shaped plug plate matches the sand-laying area.

7. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: An angle rotation mechanism is arranged at the bottom of the bearing plate, and the angle rotation mechanism comprises a support, a column and a support plate. The support plate is rotatably arranged on the column, a locking mechanism is arranged at the rotation position, and the bearing plate is connected to the support plate.

8. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 1, characterized in that: The supporting plate is provided with a plurality of liquid inlet holes, which are arranged in sequence from the near-well side to the far-well side. The liquid supply mechanism includes a pump body, a multi-way valve and a plurality of branch pipelines respectively connected to the liquid inlet holes. The plurality of branch pipelines are all connected to the pump body through the multi-way valve, the pump body is connected to the liquid tank, a main valve is provided between the pump body and the multi-way valve, and regulating valves, flow meters and pressure gauges are provided on the branch pipelines.

9. The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions according to claim 8, characterized in that: An intermediate container is provided between the pump body and the multi-way valve. The inner cavity of the intermediate container is divided into a first cavity and a second cavity by a piston. The pump body and the multi-way valve are communicated with the first cavity and the second cavity respectively.

10. A method for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions, characterized in that: The device for quantitatively characterizing the flow conductivity under non-uniform sand spreading conditions is used, and the following steps are included: S1: Laying different amounts of quartz sand in multiple sand-laying areas of the groove and covering them with a cover plate; S2: Start the liquid supply mechanism to supply liquid into the groove, and the liquid flows through the sand-laying area and then flows out from the hole; S3: The sand bed permeability and the inlet and outlet pressure difference are obtained according to the changes in the inlet and outlet liquid pressure of the groove, and the flow cross-sectional area and the length of the sand bed are obtained by using the size of the groove, and finally the flow conductivity of the sand bed is calculated; S4: Close the liquid supply mechanism, open the cover plate, and obtain the proppant migration law based on the remaining amount of quartz sand in the sand spreading area.

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